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leonid [27]
3 years ago
6

Math. ............,,,,,,,,

Mathematics
1 answer:
Sergeu [11.5K]3 years ago
5 0

Answer:

Step-by-step explanation:

ok

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Prove that there are infinitely many primes of the form 4k + 3, where k is a non-negative integer. [Hint: Suppose that there are
Simora [160]

Answer:

The prove is as given below

Step-by-step explanation:

Suppose there are only finitely many primes of the form 4k + 3, say {p1, . . . , pk}. Let P denote their product.

Suppose k is even. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).

ThenP + 2 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 2 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠2. This is a contradiction.

Suppose k is odd. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).

Then P + 4 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 4 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠4. This is a contradiction.

So this indicates that there are infinite prime numbers of the form 4k+3.

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3 years ago
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If you get this right I will mark you as a brainliest
storchak [24]

CL will always be the same as LD, the CD line is perpendicular to AB where the L is, so, the extreme points of CD will always be in the same distance of L.

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Using the formula below, find F, when f = 1000 and r = 8
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Answer: 15.625

Step-by-step explanation:

F = 1000/(8^2) = 1000/64 = 15.625

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A family has two cars. the first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of
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x + y = 60 \\ x = 60 - y
30x + 35y = 1975 \\ 30 \times (60 - y) + 35y = 1975 \\ ... \\ y = 35 \\ x = 60 - y = 60 - 35 = 25

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3 years ago
If the second hand of a clock has a length of 10 cm, find the distance the tip of the second hand travels in 45 seconds. Give an
UkoKoshka [18]

The distance traveled by the second hand of the clock is 0.471 m.

<h3 />

To calculate the distance the tip of the second hand of the clock travel in 45 seconds, we use the formula below.

<h3>Formula:</h3>
  • L = 2πr∅/360.................. Equation 1

<h3> Where: </h3>
  • L = distance traveled by the tip of the second hand.
  • r = Length of the second hand
  • ∅ = angle formed by the second hand of the clock
  • π = pie

From the question,

<h3>Given:</h3>
  • r = 10 cm = 0.1 m
  • ∅ = (360×45/60) =  270°
  • π = 3.14

Substitute these values into equation 1

  • L = 0.1×2×270×3.14/360
  • L = 0.471 cm.

Hence, The distance traveled by the second hand of the clock is 0.471 m

Learn more about distance traveled here: brainly.com/question/4931057

<h3 />

7 0
3 years ago
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